Abstract

This thesis deals with some inference problems related with inverse Gaussian models. In Chapter 2, we investigate the properties of an estimator of mean of an inverse Gaussian population that is motivated from finite population sampling [see Chaubey and Dwivedi (1982)]. We demonstrate that when the coefficient of variation is large, the new estimator performs much better than the usual estimator of the mean, namely the sample average. In Chapter 3, we provide simple approximating formulae for the first four moments of the new estimator which may be used to approximate its finite sample distribution. Chapter 4 investigates some properties of the preliminary test estimator for mean of an IG population. Such an estimator was proposed and studied in detail in the statistical literature for Gaussian and other distributions [see Bancroft (1944), Ahmed (1992)]. Our conclusions for the inverse Gaussian model are similar to the case for Gaussian model. Next, in Chapter 5, overlap measures for two inverse Gaussian densities are studied on the lines of Mulekar and Mishra (1994, 2000)